The heterogeneous nature and independent administration of geographically dispersed resources in a Grid demand the need for access control using fine-grained policies. In this paper, we investigate the problem of fine-grained access control in the context of resource allocation in the Grid, as we believe it is the first and key step in developing access control methods specifically tailored for Grid systems. To perform this access control, we design a security component (to be part of a meta-scheduler service) that finds the list of nodes where a user is authorized to run his/her jobs. The security component is designed in an effort to reduce the number of rules that need to be evaluated for each user request. We believe such a fine-grained policy-based access control would help the adoption of the Grid to a higher extent into new avenues such as desktop Grids, as the resource owners are given higher flexibility in controlling access to their resources. Similarly, Grid users get a higher flexibility in choosing the resources in which their jobs must execute.